A preliminary investigation of placement and predictors of success for students with learning disabilities in university-required mathematics courses.
Evans, Brooke
Abstract
The number of students with learning disabilities attending
institutions of higher education has dramatically increased in the last
ten years and will continue to do so. Since federal laws in the United
States and other counties require appropriate accommodations for
students with learning disabilities, it is important for universities to
evaluate the effectiveness of accommodations and services. This study
was designed to evaluate the effectiveness of a class reserved for
students with learning disabilities and to identify predictors of
success based on student documentation. Evaluation of the relationship
between student success and specific student documentation will
facilitate the development of sound, researched policies for making
accommodation and placement decisions.
Introduction
Increased attention to and legal support for those with learning
disabilities in education has led to a dramatic increase in the number
of students with learning disabilities attending colleges and
universities. Unfortunately, few institutions are monitoring
performance, graduation rates, attrition, satisfaction, or other
indicators of success for students with learning disabilities in their
learning services programs (Vogel & Adelman, 1992). Evaluation of
what little information there is available for these programs suggest
that there is reason to be concerned with success of students with
learning disabilities (Vogel & Adelman, 1992). Most universities
have ways to assess academic courses through student evaluations of
teaching but few have a system in place for feedback on their learning
services programs. This raises serious questions about the assessment
and implementation of good accommodation and placement practices and the
importance of evaluating the services that are in place.
Mathematics learning is crucial to the overall academic success of
students with learning disabilities. A significant number of students
with learning disabilities have difficulty with mathematics learning
(Miller & Mercer, 1997) and other learning disabilities may
interfere with testing ability and mathematics learning even if students
are not diagnosed with specific mathematics learning impairments
(Nolting, 2000). Students with learning disabilities are more likely to
fail to organize information, both mentally and physically, in a way
that allows for easy retrieval, use, and generalization (Scheid, 1990).
Often, students with learning disabilities achieve approximately one
year of mathematical understanding for every two years of school
attendance (Miller & Mercer, 1997). This progress continues into
adulthood, leaving students with learning disabilities behind their
contemporaries (Raskind, Goldburg, Higgins, & Herman, 1999). All of
this suggests the placement and accommodations associated with
mathematics learning are important in the success of students with
learning disabilities in higher education.
Placement and Accommodations Practices
Ofiesh and McAfee (2000) surveyed ninety-one college learning
services programs to examine current use of psycho-educational
evaluations such as the Wechsler Adult Intelligence Scale (WAIS) and the
Woodcock-Johnson Tests of Cognitive Abilities and Tests of Achievement
(WJ). They found that these tests were being consistently used for
eligibility, placement, and accommodation determinations. For
eligibility purposes, a diagnostician has a formal and systematic
process for interpreting scores supported by research.
However, the process of how test scores are being used to determine
accommodations and placement is much less structured and is widely
undocumented through survey or empirical data at the postsecondary
level. There is a strong need for further research to validate the
practice of interpreting specific parts of psycho-educational test
scores to make accommodation decisions (Ofiesh & McAfee, 2000).
These decisions are often left to a learning services specialist who
must make practical connections between test scores and available
accommodations or courses. Many learning services providers do not feel
comfortable with this process (Ofiesh & McAfee, 2000). This
discomfort is due to lack of substantiating research as well as varying
education and training levels of the providers asked to interpret
testing results. Service providers are often forced to rely solely on
their personal judgment, rather than validated criteria, when placing
students.
At lower levels of education, psycho-educational and academic test
scores are often used to place students and plan educational
interventions, but the individuals who are interpreting the scores have
an intimate relationship with the child's disability through school
records and contact with the child, parents, and teachers. This intimate
knowledge is often not available at the college level. Moreover, Ofiesh
and McAfee (2000) stress an important difference in service at the
postsecondary level: service needs to change from educational
interventions to an emphasis on independence as well as accommodations.
The psycho-educational diagnostic instruments may or may not provide the
information needed to translate to specific accommodations and to place
students in appropriate courses.
Research specific to the success of students with learning
disabilities in university-required mathematics courses is lacking.
Since the number of students with learning disabilities attending
institutions of higher education is increasing dramatically (Henderson,
2001) and learning disabilities may change into adulthood (Nolting,
2000; Maller & McDermott, 1997; Gerber, Schnieders, Patadise, Reiff,
Ginsberg, & Popp, 1990), it is important to know if university
programs are adequately accommodating these students and placing them in
courses appropriate to their needs.
Method
The goal of this study was to evaluate the effectiveness of a class
reserved for students with learning disabilities and to make
recommendations for placement criteria. The researcher hopes that using
results from data that is readily available and provided to the
university and the support services for students with learning
disabilities will improve placement and accommodations decisions in
university-required mathematics courses.
The population for this study is a group of students identified as
having a learning disability who attended a university in the US between
1998-2002. These students had been diagnosed as having a learning
disability by a licensed specialist and had used the academic support
services at the university. The population selected consisted of 143
students who had full documentation and had taken the
university-required mathematics course.
The research was conducted in three parts and included both
qualitative and quantitative methods in analyzing student success (a
grade of C or 2.0 on a 4.0 scale) in university-required mathematics
courses. After approval from the university, data collection began with
student information obtained through the Department of Mathematics and
Statistics, Academic Support Center, and Enrollment Services.
The first part of the study examined success in the course
enrolled. All students take a mathematics placement exam to ensure
enrollment in an appropriate course. Of those who place in the
lowest-level courses which will fulfill the university mathematics
requirement, students have the choice of enrolling in one of two College
Algebra-level courses: an open section of Finite Mathematics (Finite) or
an open section of Elementary Mathematical Models (EMM). Students with
learning disabilities may enroll in any open section but also have the
option of enrolling in a special section of Elementary Mathematical
Models reserved for students with learning disabilities (EMM-LD). The
students served in these courses usually have at least one year of
algebra in high school but are not necessarily headed for calculus. Both
courses prepare students to go on to pre-calculus and calculus. They
cover the same basic mathematical concepts but with very different
approaches, one being a non-traditional mathematical modeling course and
the other a traditional mathematics course. The non-traditional
mathematical modeling course tends to look at the bigger picture and
helps students to use their intuition in solving mathematical problems.
The course is designed to teach students the mathematical concepts and
language they need to succeed in this course as well as in general
education classes such as economics, statistics, and chemistry. The
traditional course is very textbook driven and consists of learning
formulas and answering questions. Student performance in each of the
three courses, EMM-LD, EMM, and Finite, was analyzed.
The second part of the research involved examining student
documentation for predictors of student success for the course in which
they were enrolled. Student documentation included: SAT scores;
high-school GPA; high-school transcript information; full-scale
intelligence and achievement test scores; gender; and grades in
university-required mathematics courses. These previously identified
variables were analyzed, individually and in combinations, for predictor
variables for the students' performance in their
university-required mathematics course. Regression analysis was used to
explore variance in performance among the students.
The final part of the study was a survey of student satisfaction
with accommodations in their university-required mathematics course. The
survey was a small sampling of the population of students with learning
disabilities who took the university-required mathematics course and was
conducted through self-selection only. This qualitative data provided
information on student perceptions of their experiences in
university-required mathematics courses and the accommodations afforded
them within the university.
Results
The researcher first examined the performance of students with
learning disabilities overall and within the courses taken (see Table 1)
using univariate analysis of variance and regression analysis testing
where appropriate. The study population of 143 students with documented
learning disabilities included 70 students enrolled in an open section
of Finite Mathematics, 18 students in an open section of Elementary
Mathematical Models, and 55 students in the section of Elementary
Mathematical Models reserved for students with learning disabilities.
Students enrolled in the reserved section (EMM-LD) performed
significantly better (p=.003) than their peers enrolled in the open
sections. The proportion of students enrolled in EMM-LD with passing is
significant within the study group (All) (z=1.75, p=.0401).
Approximately ninety-five percent of the students with learning
disabilities in this section earned a grade of C or better (2.0 on a 4.0
scale) and the average grade for students with learning disabilities
enrolled in this section was a B (3.13 on a 4.0 scale). Enrollment in
the open sections of Finite and EMM is not significant (p=.947), which
suggests that the students enrolled in the open sections perform
similarly, with a grade of C or 2.46 and 2.44 (on a 4.0 scale)
respectively. Enrollment in EMM-LD is significant when compared to the
open sections of EMM (p=.032) and Finite (p=.001) individually.
Since students with learning disabilities perform significantly
better in the reserved section, which suggests that the class format is
important to their success, it is important to examine the differences
between the reserved section and the open sections. All of the Finite
Mathematics courses take a common final and have a set curriculum. The
Elementary Models courses do not have a common final but follow the same
basic curriculum. A quick review of the finals for all of the Elementary
Models courses, including the LD course, did not reveal any significant
differences in the amount or difficulty of the course material covered.
The major differences between the reserved section of Elementary Models
and the open sections of Finite Mathematics and Elementary Models are
the limited enrollment, which allows for more personalized attention,
and access to a class mentor. The class mentor meets with students on a
regular basis to discuss class ideas, note-taking strategies, and
general mathematics questions. The reserved section also meets three
times a week, which gives students fifty minutes of instruction a week
more than some of the open enrollment courses. All students with
learning disabilities, regardless of course enrolled, are afforded
general accommodations as recommended by their diagnostic specialist
including, but not limited to, extended time on tests, a note taker, and
a quiet place to take tests. The results of this study also suggest that
students with learning disabilities tend to perform better in a
non-traditional modeling course than they do in a traditional
mathematics course.
The researcher next investigated predictors of student success
(defined as the students' final grade in the university-required
mathematics course), overall and within the courses taken, for each of
the specified variables individually and in various combinations. Since
reserved sections are not always available, it is important to know if
students of a certain profile would have more chances for success if
placed in a particular type of course and if the currently used
placement criteria are sufficient in this manner. The first group of
combinations tested included high-school transcript information, gender,
SAT scores, and university-required mathematics course enrollment. Next,
the researcher chose to look at combinations of these tests individually
with selected variables from the first combination of high-school
transcript information.
Overall, students with learning disabilities who performed well in
eleventh-grade English, twelfth-grade English, and the Broad Written
Language subtest of the Woodcock-Johnson Test (WJ), individually, may
perform well in any section of the university-required mathematics
course (see Table 2). The combination of enrollment in the Reserved
Section of Elementary Models, ninth-grade mathematics performance, Broad
Reading score (WJ), and eleventh-grade English performance was also
shown to be significant in predicting student performance in
university-required mathematics.
For students enrolled in open sections of Finite Mathematics,
twelfth-grade English was the only individually significant predictor of
student success (see Table 3). Students with high twelfth-grade English
grades tend to also do well in Finite Mathematics. The most significant
combination model to predict the success of students enrolled in Finite
Mathematics includes performance in eleventh-grade mathematics and the
Mathematics SAT score, although only eleventh-grade mathematics was the
individually significant factor within the model and the Mathematics SAT
score had a negative coefficient within the model.
Students with learning disabilities who perform well in ninth-grade
mathematics, eleventh-grade English, twelfth-grade English, Vocabulary,
and Applied Problems individually were significantly more likely to
perform well in any section of Elementary Models than those students who
did not perform well in these areas (see Table 4). The most significant
combination model to predict student success for all sections of
Elementary Models includes ninth-grade mathematics performance,
eleventh-grade English performance, verbal SAT score, and the Full Scale
IQ score from the WAIS. All the variables in the combination had
positive coefficients within the model except Full Scale IQ.
Female students tend to get better grades than male students in the
open sections of Elementary Models (see Table 5). The only other
individual predictors for this section are within the Woodcock-Johnson
subtests but, since few students from this group reported these scores,
these results cannot be stated with confidence and are for reference
only. Students with high Calculation (WJ), Applied Problems (WJ), and
Dictation (WJ) subtest scores may perform well in the open sections of
Elementary Models. The most significant combination to predict student
success in the open sections of Elementary Models includes Performance
IQ (WAIS), Verbal IQ (WAIS), overall high-school GPA, eleventh-grade
mathematics performance, eleventh-grade English performance and gender.
For the gender coefficient in the model, female students outperformed
male students. Also, performance in eleventh-grade mathematics and
eleventh-grade English had negative coefficients within the model. All
the other in the combination model coefficients were positive. The
researcher was not able to include the WJ-R in the combinations for the
open sections of Elementary Models because there were too few reported
cases.
Students who were successful in the reserved section of Elementary
Models may have also performed well in ninth-grade mathematics,
tenth-grade mathematics, tenth-grade English, eleventh-grade English,
and twelfth-grade English (see Table 6). There were two highly
significant combination models to predict student success in the
reserved sections of Elementary Models. The first includes
eleventh-grade English performance, ninth-grade mathematics performance,
and ninth-grade English performance. Within this combination model,
ninth-grade English performance and tenth-grade mathematics performance
had negative coefficients. The second significant model includes gender,
Broad Reading (WJ), Broad Mathematics (WJ), letter-word identification
(WJ), passage comprehension (WJ), ninth-grade English performance,
tenth-grade English performance, and eleventh-grade English performance.
Within this combination model, female students outperformed male
students and the Broad Mathematics score, letter-word identification
score, and passage comprehension score had negative coefficients.
It is interesting to note that in no case, overall or within
groups, did SAT Scores or overall high-school GPA present itself as an
individually significant predictor of student success in
university-required mathematics courses. Also, the most commonly used
measure for placing students, mathematics course and test information,
was not shown to be a good predictor of how a student will perform.
Gender (females outperforming males) was shown to be a significant
predictor for students success in the open sections of Elementary
Mathematical Models but not for the reserved sections.
It is important to note that the Academic Support Center places
many of the students in the mathematics course they feel is most
appropriate given their learning disability profile. The factors
considered for placement include, but are not limited to: WAIS Verbal IQ
and Performance IQ; high-school math courses; WJ-R Calculation, Applied
Problems, and reading subtests; and the student's report of
strengths and weaknesses. Analysis of these placement factors showed no
significant influence on student final grades in the mathematics course.
However, since these factors affect placement and placement affects the
final grade, it is import not to neglect the importance of these
factors.
Finally, student satisfaction with accommodations in their
university-required mathematics courses was tested. Overall, students
with learning disabilities are satisfied with the accommodations they
receive. Also, there is no significant difference in satisfaction
between the students with learning disabilities in the reserved section
of Elementary Models and the students with learning disabilities in open
sections of Finite Mathematics and Elementary Models. This suggests that
students with learning disabilities are receiving the accommodations
they feel are necessary in all section of university-required
mathematics.
Conclusions
Based on the results of this study, there are some important
implications for many different groups within the university. Academic
support services and those who make accommodation and placement
recommendations should note that student documentation that is readily
available to them can and should be used to support accommodations and
placement of students into appropriate mathematics courses.
Statistically significant predictors of student success were identified
in this study which did not necessarily include the items widely thought
to predict student success and used to place students, including many
mathematics scores. SAT scores, overall GPA, and many of the achievement
and intelligence test and subtest scores. This suggests that current
placement and accommodation criteria should be further analyzed for
validity.
Also, for university departments of mathematics, students with
learning disabilities perform better in the non-traditional modeling
course and significantly better in the reserved section, which suggests
that the different learning approach and extra accommodations associated
with this course are beneficial to their performance. Perhaps more
universities should consider offering such courses.
For all involved in the mathematical education of students with
learning disabilities, high-school English and, therefore, reading
comprehension present themselves as significant factors in the success
of students overall and within groups, while mathematics scores were
much less significant, which highlights the importance of language and
communication skills for students with learning disabilities enrolled in
any section of university-required mathematics.
Implications for Future Research
Based on the results of this study, the researcher believes there
are several courses available for additional research in this area. This
study was limited to the data available for students with learning
disabilities with full documentation who had taken one of the
university-required mathematics courses at a particular university
during a four-year time period. This certainly limits the number of
participants and the amount of usable data. The researcher would
recommend a larger study involving various universities. With a larger
study, a researcher could also examine more closely predictors for
various types of learning disabilities and the effectiveness of specific
accommodations and be more confident in making generalizations to other
programs.
This research was also limited in that there was no data on the
amount and type of services utilized by students or when the students
disclosed their learning disability to the university and requested
services. The researcher would recommend a study to examine the effect
these factors on student performance in university-required mathematics
courses.
Also, the survey of satisfaction component to this study was
limited to a self-selected group of students surveyed after completing
the course and receiving a grade. Their perceptions of how well they
were accommodated may have been influenced by their final grade in the
course. They students may have also forgotten many of the accommodations
afforded them by the time they completed the survey. The researcher
recommends a study of LD student satisfaction with accommodations where
the survey is given to all students before the end of the course in a
manner similar to course evaluations.
Reading comprehension and high-school English scores emerged as
significant predictors of LD student success in university-required
mathematics courses. This suggests that more research needs to be
conducted on the importance of reading comprehension in university-level
mathematics courses as well as how to compensate for deficiencies in
this area.
Selected References
Alster, E.H. (1997). The effects of extended time on algebra test
scores for college students with and without learning disabilities.
Journal of Learning Disabilities, 30(2), 222-227.
Gerber, P.J., Schnieders, C.A., Patadise, L.V., Reiff, H.B.,
Ginsberg, R.J., & Popp, P.A. (1990). Persisting problems of adults
with learning disabilities: Self-reported comparisons from their
school-age and adult years. Journal of Learning Disabilities, 23(9),
570-573.
HEATH Resource Center. (n.d.). Success in college for adults with
learning disabilities. HEATH Resource Center: The National Clearing
House on Postsecondary Education for Individuals with Disabilities.
Retrieved December 17, 2001, from http://www.heath.gwu.edu/Success.html
Henderson, C. (2001). College freshmen with disabilities: A
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Education.
LaMorte, M.W. (2002). School law: Cases and concepts. Boston:
Massachusetts: A Pearson Education Company.
Maller, S.J., & McDermott, P.A. (1997). WAIS-R profile analysis
for college students with learning disabilities. School Psychology
Review, 26(4), 575-585.
Miller, S.P., & Mercer, C.D. (1997). Educational aspects of
mathematics disabilities. Journal of Learning Disabilities, 30(1),
47-56.
National Joint Committee on Learning Disabilities (NJCLD). (1999,
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Nolting, P.D. (2000). Mathematics and learning disabilities
handbook: Guide to processing deficits and accommodations. Bradenton,
FL: Academic Success Press.
Ofiesh, N.S., & McAfee, J.K. (2000). Evaluation practices for
college students with L.D. Journal of Learning Disabilities, 33(1),
14-25.
Raskind, M.H., Goldburg, R.J., Higgins, E.L., & Herman, K.L.
(1999). Patterns of change and predictors of success in individuals with
learning disabilities: Results from a twenty-year longitudinal study.
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Brooke Evans, Ph.D.
The Metropolitan State College of Denver
Table 1. LD Student Success in the University-Required Mathematics
Course.
Mean Class Grade Point Proportion of Students with
Course Average (GPA) Passing Grades(n)
All 2.71 .88 (143)
Finite 2.44 .86 (70)
EMM 2.46 .78 (18)
EMM-LD 3.13 .95 (55)
Table 2. Predictors of Student Success, All LD Students (n=143)
Variable Tested Significance
Eleventh-Grade English Performance p=.048
Twelfth-Grade English Performance p .001
Broad Written Language WJ Score p=.035
Combination of enrollment in the Reserved Section of p=.017
Elementary Models, ninth-grade mathematics, Broad
Reading WJ, and eleventh-grade English
Table 3. Predictors of Student Success, Finite Mathematics (n=70)
Variable Tested Significance
Twelfth-Grade English Performance p=.006
Combination of mathematics SAT scores and eleventh-grade p=.014
mathematics performance
Table 4. Predictors of Student Success, All Sections of EMM (n=73)
Variable Tested Significance
Ninth-Grade Mathematics Performance p=.019
Eleventh-Grade English Performance p=.009
Twelfth-Grade English Performance p=.002
Vocabulary Score p=.036
Applied Problems Score p=.026
Combination of ninth-grade mathematics performance, p=.003
eleventh-grade English performance, verbal SAT score,
and the Full Scale IQ Score
Table 5. Predictors of Student Success, Open Sections of EMM (n=18)
Variable Tested Significance
Gender p=.004
Calculation WJ* Score p=.032
Applied Problems WJ* Score p=.012
Dictation WJ* Score p=.04
Combination of WAIS Performance IQ Score, WAIS Verbal p=.025
IQ Score, Eleventh-Grade Mathematics Performance,
Eleventh-Grade English Performance, Overall High-School
GPA, and Gender
*Not enough data to be reported with confidence--for reference only
Table 6. Predictors of Student Success, Reserved Section of EMM (n=55)
Variable Tested Significance
Ninth-Grade Mathematics Performance p .001
Tenth-Grade Mathematics Performance p=.032
Tenth-Grade English Performance p=.008
Eleventh-Grade English Performance p=.001
Twelfth-Grade English Performance p=.003
Combination of eleventh-grade English performance, tenth- p=.001
grade mathematics performance, tenth-grade English
performance, ninth-grade mathematics performance, and
ninth-grade English performance
Combination of gender, Broad Reading Score (WJ), Broad p .001
Mathematics Score (WJ), letter-word identification score
(WJ), passage comprehension score (WJ), ninth-grade
English performance, tenth-grade English performance,
and eleventh-grade English performance.
